Answer: 20/101
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Step-by-step explanation:
The sine ratio involves the opposite side over the hypotenuse
For reference angle E, the opposite side is the unknown vertical side, which we'll call x for now.
The known leg is 99 and the known hypotenuse is 101. We'll use these two bits of info to find x. Apply the pythagorean theorem:
a^2 + b^2 = c^2
x^2 + 99^2 = 101^2
x^2 + 9801 = 10201
x^2 = 10201-9801
x^2 = 400
x = sqrt(400)
x = 20
The missing vertical side of the triangle is 20 units. Now we can apply the sine ratio to find sin(E)
sin(angle) = opposite/hypotenuse
sin(E) = 20/101
This fraction cannot be reduced further. This is because 20 = 2*2*5, and neither 2 nor 5 is a factor of 101.